Question

Упростите выражение:
а) $frac{2c}{b+c}- frac{(b-c)^{2}}{b}( frac{b}{(c-b)^{2}}+ frac{b}{b^{2}-c^{2}})$
б) $( frac{x}{ x^{2} -y^{2}}- frac{x}{(x-y)^{2}}) frac{(y-x)^{2}}{2x}- frac{x}{x+y}$

Answer 1

1
1)b/(b-c)²+b/[(b-c)(b+c)]=b(b+c+b-c)/[(b-c)²(b+c)]=2b²/[(b-c)²(b+c)]
2)(b-c)²/b*2b²/[(b-c)²(b+c)]=2b/(b+c)
3)2c/(b+c)-2b/(b+c)=(2c-2b)/(b+c)=2(c-b)/(b+c)
2
1)x/[(x-y)9x+y)]-x/(x-y)²=x(x-y-x-y)/[(x-y)²(x+y)]=-2xy/[(x-y)²(x+y)]
2)-2xy/[(x-y)²(x+y)]*(y-x)²/2x=-y/(x+y)
3)-y/(x+y)-x/(x+y)=(-y-x)/(x+y)=-(y+x)/(x+y)=-1